The main objective of this work is to develop a statistical algorithm to process the data generated by the Large-Eddy-Simulation model (LES) in real time. The simulations analyzed here were based on a convective, neutral and stable periods. Mainly the temperature and velocity components were analyzed. The new statistical algorithm generates all the first and second order statistic moments for “u,v,w, ¿ ,q”, and the components of TKE equation budget. All these parameters were developed to the resolved and sub-grid scales and indicate agreement with the expected profile

Barbaro, E.W.

Oliveira, A.P.

Soares, J.

English

Wageningen Yield 

                          VI Workshop Brasileiro de Micrometeorologia                                  233
Validation of a statistc algorithm applied to LES model -
Part 1: First and second order statistcs
Eduardo Wilde Bárbaro, Amauri Pereira de Oliveira,
Jacyra Soares
 Institute of Astronomy, Geophysics and Atmospheric Sciences/University of São Paulo
e-mail:  eduardo.barbaro@usp.br
Abstract
The main objective of this work is to develop a statistical
algorithm to process the data generated by the Large-Eddy-Simulation
model (LES) in real time. The simulations analyzed here were based on
a convective, neutral and stable periods. Mainly the temperature and
velocity components were analyzed. The new statistical algorithm
generates all the first and second order statistic moments for “u,v,w,θ ,q”,
and the components of TKE equation budget. All these parameters were
developed to the resolved and sub-grid scales and indicate agreement
with the expected profiles.
Resumo
O objetivo principal deste trabalho é desenvolver um algoritmo
estatístico com o intuito de processar as saídas do modelo Large-Eddy-
Simulation (LES) em tempo real. As simulações analisadas foram para
os períodos convectivo, neutro e estável. Principalmente a temperatura a
umidade específica e as componentes da velocidade serão analisadas. O
novo algoritmo gera todos os momentos estatísticos de primeira e se-
gunda ordem para “u,v,w,θ ,q”, e as componentes da equação do balanço
de energia cinética turbulenta. Todos os parâmetros foram desenvolvi-
dos para a escala resolvida e subgrade. Os perfis verticais para todas as
variáveis foram reproduzidos com sucesso validando assim o algoritmo
para estas configurações.
Introduction
Numerical modeling has been one of the most useful tools to
understand the PBL behavior, Saiki, et.al. (2000). Large-Eddy Simulation
models (LES) are the most advanced technique available to simulate
turbulence. The LES code used in this work was proposed by Moeng
234                                             CiŒncia e Natura Especial, UFSM
(1984) and improved by Sullivan, et.al. (1994), mainly in the 2-steps
subgrid scheme. Understanding this kind of model, it is possible to
simulate several conditions of the planetary boundary layer (PBL) over
stable, neutral or convective situations. see Moeng, (1994) for a convective
PBL, Saiki et.al. (2000) and Kosovic et.al. (2000) for neutral and stable
cases.
The main objective of this work (part I) is to use the LES model
to characterize the PBL first and second-order statistic moments in a
convective, neutral and stable conditions, over a horizontally
homogeneous domain. To accomplish that, a real time statistic algorithm
was developed and implement inside the code to eliminate the post-
processing. The part II of this work will discuss the TKE budget over
the stable, neutral and convective cases.
Methodology
The computations presented here were performed on a 5x5x2Km
domain for convective case and 1x1x1Km for the neutral and stable ones.
All simulations use 963 grid points evenly spaced. More details about
the simulations can be found in Moeng, et.al. (1994), for the convective
case and in Saiki et.al. (2000) for the neutral and stable situations.
In the convective case, 2.5 hours of PBL was simulated. In the
second one, a 3 hours neutral and 11 hours stable PBL were simulated
sequentially. The computer processing time is respectively about 4.5 hours,
13 hours and 60 hours. All the numerical simulations were run using a
DELL-R900 Intel 2-quad (8 cores total) 12 Gb RAM and 1.2 Tb HD.
The new algorithm implemented in the LES model consists in a
real time TKE budget, momentum, humidity and temperature
calculations. The horizontal fluxes and the characteristic scale time
evolutions were implemented. All the improvements were developed to
the sub grid scale too. It is important to say that the computation time
did not grow with the new improvements in the code.
In this work an especial overview will be given to the temperature
and velocity profiles and second-order statistics.
Results
The Figure 1 shows the mean temperature and velocity vertical
profiles. The Figure 2 shows the second-order velocity, u and v
components, and temperature vertical profiles, only for convective and
stable cases.
                          VI Workshop Brasileiro de Micrometeorologia                                  235
Figure 1. (a) Mean temperature vertical profile, convective (red), neutral (blue) and stable
(black) simulations and (b) mean velocity vertical profile, convective, neutral and stable
simulations. These results are displayed to the last simulations time-step.
The temperature and velocity profiles presented in the figure 1
show agreement with the previous papers. The low level jet can be
visualized in the figure 1b during the stable period. In the neutral situation
the mixed layer can be visualized. The temperature inversion either can
be observed. In the PBL top a strong <u Ł > and <v Ł >
intensification can be observed in the convective case. This intensification
cannot be observed in the stable profiles. The subgrid results are not
significative in the horizontal statistics.
Figure 2. (a) Second-order velocity vertical profile, convective (red) and stable (black)
cases and (b) second-order temperature profile, convective and stable cases. These results
are displayed to the last simulations time-step.
 
 
236                                             CiŒncia e Natura Especial, UFSM
Conclusion
These results indicate that the statistic algorithm performs
satisfactorily in all the PBL situations presented in this work. The results
were compared with the original papers with agreement. The subgrid
implementations show concordance with these articles ensuring the
algorithm.
Bibliography
MOENG, C-H. A Large Eddy Simulation Model for the Study of
Planetary Boundary Layer Turbulence. Journal of the Atmospheric.
Sciences. 41-13: 2052-2062, 1984.
MOENG, C-H., SULLIVAN, P.P. A Comparison of shear- and
buoyancy-driven Planetary Boundary Layers Flows, Journal of
Atmospheric Sciences 51-7 999-1022, 1994.
SULLIVAN, P.P., McWILLIAMS, J.C., MOENG, C-H. A Subgrid-
Scale Model For Large-Eddy Simulation of PBL Flows, Boundary
Layer Meteorology 71 247-276, 1994.
KOSOVIC, B., CURRY, J.A. A Large Eddy Simulation Study of a
Quasi-Steady, Stably Stratified Atmospheric Boundary Layer.   J. of the
Atmospheric Sciences 57 1052-1068, 1999.
SAIKI, E.M., MOENG, C-H., SULLIVAN, P.P. Large-Eddy
Simulation of the Stably Stratified Planetary Boundary Layer.
Boundary-Layer Meteorology  95 1-30, 2000.


A Comparison of shear- and buoyancy-driven Planetary Boundary Layers Flows,

A Large Eddy Simulation Model for the Study of Planetary Boundary Layer Turbulence.

A Large Eddy Simulation Study of a Quasi-Steady, Stably Stratified Atmospheric Boundary Layer.

A SubgridScale Model For Large-Eddy

Validation of a statistic algorithm applied to LES model - Part I: First and second order statistics

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Validation of a statistic algorithm applied to LES model - Part I: First and second order statistics

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